# Pre Calculus

Let $\bold{w} = \begin{pmatrix} 2 \\ -1 \end{pmatrix}$. There exists a $2 \times 2$ matrix $\bold{P}$ such that
$\text{proj}_{\bold{w}} \bold{v} = \bold{P} \bold{v}$
for all 2-dimensional vectors $\bold{v}$. Find $\bold{P}$.

1. 👍 0
2. 👎 0
3. 👁 260
1. can you skip the LaTex? It appears that you are saying that

w = (2,1) and there is a 2x2 P such that
w•v = Pv

or something like that. Correct?

1. 👍 0
2. 👎 0
posted by Steve

## Similar Questions

Find the $2 \times 2$ matrix $\bold{A}$ such that $\bold{A} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$ and $\bold{A} \begin{pmatrix} 0 \\ 1 \end{pmatrix} = \begin{pmatrix} -7 \\ 4 asked by Zheng on February 25, 2017 2. ### Pre Calculus For a vector \bold{v}, let \bold{r} be the reflection of \bold{v} over the line \[\bold{x} = t \begin{pmatrix} 2 \\ -1 \end{pmatrix}.$ [asy] unitsize(1 cm); pair O, V, R; O = (0,0); V = (3,1); R = reflect(O,(2,-1))*(V);

asked by Bob on September 20, 2017

Find the $2 \times 2$ matrix $\bold{A}$ such that $\bold{A} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$ and $\bold{A} \begin{pmatrix} 0 \\ 1 \end{pmatrix} = \begin{pmatrix} -7 \\ 4 asked by Zheng on February 22, 2017 4. ### Math Find the 2 \times 2 matrix \bold{A} such that \[\bold{A} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$ and $\bold{A} \begin{pmatrix} 0 \\ 1 \end{pmatrix} = \begin{pmatrix} -7 \\ 4 asked by Zheng on February 23, 2017 5. ### Precalculus Compute the distance between the parallel lines given by \[\begin{pmatrix} 1 \\ 4 \end{pmatrix} + t \begin{pmatrix} 4 \\ 3 \end{pmatrix}$ and $\begin{pmatrix} -5 \\ 6 \end{pmatrix} + s \begin{pmatrix} 4 \\ 3 \end{pmatrix}.$

asked by Zheng on February 13, 2017
6. ### Precalculus

The vector $\begin{pmatrix} k \\ 2 \end{pmatrix}$ is orthogonal to the vector $\begin{pmatrix} 3 \\ 5 \end{pmatrix}$. Find $k$. I thought the answer should be 10/4/

asked by Zheng on February 8, 2017
7. ### Precalculus

Latex: The vector $\begin{pmatrix} k \\ 2 \end{pmatrix}$ is orthogonal to the vector $\begin{pmatrix} 3 \\ 5 \end{pmatrix}$. Find $k$. Regular: The vector , is orthogonal to the vector . Find k. I can't seem to figure it out, I

asked by Zheng on February 9, 2017
8. ### Pre Calculus

Find all $2 \times 2$ matrices $\bold{A}$ that have the property that for any $2 \times 2$ matrix $\bold{B}$, $\bold{A} \bold{B} = \bold{B} \bold{A}.$

asked by Bob on September 20, 2017
9. ### Algebra

Round each number to the place value indicated by the digit in bold. A: 3587 5 is bold. B: 148213 the first one, one is bold. C: 23785 3 is bold. D: 2357 5 is bold.

asked by Kali G on September 10, 2014
10. ### Language Arts

Directions: replace the bold faced word with a contraction. 1. We will(bold faced) see you t the English class next week! Answer: We'll 2. There is (bold faced) no milk in the refrigerator. Answer: There's 3. There will (bold

asked by Patrick on March 2, 2016

More Similar Questions